Much of the answer lies in the age of the cabinets. If they were built before 1956, the clear coat on them will be real varnish, in which case simply cleaning them with a strong solution of TSP (dissolved in water) will dull the gloss sufficiently for the paint to stick well. Otherwise you need to sand down the surface of the cabinet doors for the new paint to stick well. (Alternatively, you can use a chemical deglosser called "Liquid Sandpaper" to degloss polyurethane and alkyd paints.) Don't forget to remove any residual TSP with clean rinse water before painting.

Also, if you intend to paint the interior of the cabinets, then use a paint that dries to a HARD film on the cabinet shelves. Working surfaces like floors, table tops, counter tops, window sills, mantles, etc. need to have hard surfaces to prevent being scratched up and having dirt embedded in them, causing them to show traffic patterns and wear much sooner. I own a small apartment block and I use Benjamin Moore "Melamine" in the 303-90 tint base on all my cabinet, cupboard and closet shelves. This product is an alkyd paint with polyurethane resins added to it to make it dry harder than a regular alkyd wall paint.

You don't need to know the rest

You see, the Bayer Company (the Aspirin people) were the first to patent the modification of an alkyd resin by adding di- and tri- isocyanates to the alkyd. Isocyanates are chemicals that have a -N=C=O group in them. These isocyanate groups will react with hydroxyl groups (-OH) to form urethane linkages inside the alkyd resin like this:

A-N=C=O plus HO-B gives A-(NH)-(C=O)-O-B

and that ugly thing between the A and B is a urethane group.

Urethane groups are very strong, and they act inside the alkyd resin very much like a roll cage inside a racing car, making the alkyd resin much harder if you tried to crush it, and much stiffer if you tried to stretch it. As a result, "urethane modified alkyds" (which have since come to be called "polyurethane") dry to harder and stronger films than regular alkyd wall paints.

Bayer patented the urethane modification of alkyd resins in 1956, so it's a safe bet that any clear coat over wood that was applied prior to 1956 would have been a normal varnish.

And, of course, normal varnish is chemically very similar to drying oil based paints. Since TSP dulls the gloss of drying oil based paints, it will dull the gloss of real varnish as well.

There are very many different kinds of polyurethane. Any polymer that has those urethane groups in it is a "polyurethane". So, I will typically refer to the polyurethanes used as varnish and hardwood floor finishes as "alkyd based polyurethane".